Six desirable characteristics of routine marking movement toward explorative participation¶

Theory · All theories
Evidence · 1 claim (1 for) · 1 study (1 qualitative), q3 · 0 of 1 report an effect size · 1 claim rests on one study

Description¶

The paper presents, in Table 1, a list of observed changes in learners' performance that indicate a move toward explorative participation, drawn from Lavie et al. (2019) and earlier empirical works: flexibility (performing a task in more than one way), bondedness (each step of a procedure feeds the next), applicability (isolating a performance and applying it on different occasions), performer's agentivity (making more decisions during learning), objectification (increasing the level of abstraction of a mathematical object), and substantiability (establishing criteria to assess one's own outcome). These changes occur when the learner's attention shifts from the performance as such to its outcome.

Design Implications¶

Context¶

Requirements¶

• Observation of learners' performance over time to detect changes in these characteristics

Constraints¶

• In empirical research, pure rituals or pure explorations rarely appeared; outcomes were not always separable from the specific procedure followed

Target Learners¶

• university mathematics students
• school mathematics students

Target Goals¶

• de-ritualization of routines
• explorative participation in mathematical discourse

Claims¶

• Numerical routines individualize through a three-stage sequence of vertical and horizontal bonding [+W]

Related Patterns¶

Examples¶

• Analyze lecturers' proof discourse for flexibility, bondedness, applicability, agentivity, objectification, and substantiability to study de-ritualization opportunities

Key Sources¶

• Karavi, Mali, & Avraamidou. (2022). Commognition as an approach to studying proof teaching in university mathematics lectures. EURASIA Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/12173